Nevertheless, Mr. Mead, a Republican, has ordered his top environmental officials to prepare to comply with the president’s effort, known as the Clean Power Plan — to prepare for a future in which Mr. Obama’s climate change rules prevail and the country’s coal market is nearly frozen. Wyoming is one of at least 20 states that are moving forward with efforts to comply with the rules or to analyze alternative plans. Several of these states are also suing to stop the rules, according to experts who track state climate change policy.

“Obviously we’re suing and going to fight,” Mr. Mead, a former United States attorney for Wyoming, said in an interview in his office here. “But from my court experience, I know you have to prepare not to win.”